// C++ Program for Dijkstra's dial implementation
#include<bits/stdc++.h>
using namespace std;
# define INF 0x3f3f3f3f
 
// This class represents a directed graph using
// adjacency list representation
class Graph
{
    int V;  // No. of vertices
 
    // In a weighted graph, we need to store vertex
    // and weight pair for every edge
    list< pair<int, int> > *adj;
 
public:
    Graph(int V);  // Constructor
 
    // function to add an edge to graph
    void addEdge(int u, int v, int w);
 
    // prints shortest path from s
    void shortestPath(int s, int W);
};
 
// Allocates memory for adjacency list
Graph::Graph(int V)
{
    this->V = V;
    adj = new list< pair<int, int> >[V];
}
 
//  adds edge between u and v of weight w
void Graph::addEdge(int u, int v, int w)
{
    adj[u].push_back(make_pair(v, w));
    adj[v].push_back(make_pair(u, w));
}
 
// Prints shortest paths from src to all other vertices.
// W is the maximum weight of an edge
void Graph::shortestPath(int src, int W)
{
    /* With each distance, iterator to that vertex in
       its bucket is stored so that vertex can be deleted
       in O(1) at time of updation. So
    dist[i].first = distance of ith vertex from src vertex
    dits[i].second = iterator to vertex i in bucket number */
    vector<pair<int, list<int>::iterator> > dist(V);
 
    // Initialize all distances as infinite (INF)
    for (int i = 0; i < V; i++)
        dist[i].first = INF;
 
    // Create buckets B[].
    // B[i] keep vertex of distance label i
    list<int> B[W * V + 1];
 
    B[0].push_back(src);
    dist[src].first = 0;
 
    //
    int idx = 0;
    while (1)
    {
        // Go sequentially through buckets till one non-empty
        // bucket is found
        while (B[idx].size() == 0 && idx < W*V)
            idx++;
 
        // If all buckets are empty, we are done.
        if (idx == W * V)
            break;
 
        // Take top vertex from bucket and pop it
        int u = B[idx].front();
        B[idx].pop_front();
 
        // Process all adjacents of extracted vertex 'u' and
        // update their distanced if required.
        for (auto i = adj[u].begin(); i != adj[u].end(); ++i)
        {
            int v = (*i).first;
            int weight = (*i).second;
 
            int du = dist[u].first;
            int dv = dist[v].first;
 
            // If there is shorted path to v through u.
            if (dv > du + weight)
            {
                // If dv is not INF then it must be in B[dv]
                // bucket, so erase its entry using iterator
                // in O(1)
                if (dv != INF)
                    B[dv].erase(dist[v].second);
 
                //  updating the distance
                dist[v].first = du + weight;
                dv = dist[v].first;
 
                // pushing vertex v into updated distance's bucket
                B[dv].push_front(v);
 
                // storing updated iterator in dist[v].second
                dist[v].second = B[dv].begin();
            }
        }
    }
 
    // Print shortest distances stored in dist[]
    printf("Vertex   Distance from Source\n");
    for (int i = 0; i < V; ++i)
        printf("%d     %d\n", i, dist[i].first);
}
 
// Driver program to test methods of graph class
int main()
{
    // create the graph given in above fugure
    int V = 9;
    Graph g(V);
 
    //  making above shown graph
    g.addEdge(0, 1, 4);
    g.addEdge(0, 7, 8);
    g.addEdge(1, 2, 8);
    g.addEdge(1, 7, 11);
    g.addEdge(2, 3, 7);
    g.addEdge(2, 8, 2);
    g.addEdge(2, 5, 4);
    g.addEdge(3, 4, 9);
    g.addEdge(3, 5, 14);
    g.addEdge(4, 5, 10);
    g.addEdge(5, 6, 2);
    g.addEdge(6, 7, 1);
    g.addEdge(6, 8, 6);
    g.addEdge(7, 8, 7);
 
    //  maximum weighted edge - 14
    g.shortestPath(0, 14);
 
    return 0;
}
